Amanda Greer said she was “shocked, furious and confused” when she heard Henry had a history of violence.
She welcomed the FAI and said she hoped there would be “answers on the horizon”.
It comes after campaigners called for greater use of location tracking technology to monitor high-risk suspects on bail.
An online petition was launched in August, calling for a “Stacy’s law” in memory of Stacy Hunter who was killed at her home near Houston in Renfrewshire by her estranged husband while he was on bail.
Scottish ministers have previously faced criticism over the slow rollout of Global Positioning System (GPS) equipment, which is used far less in Scotland than in some other countries.
Last month, First Minister John Swinney said GPS tracking of people on bail would begin in parts of central Scotland next year.
The Greer family’s solicitor Gordon Dalyell, from Digby Brown, said: “What happened to Daniel was utterly horrific and the strength of character that Amanda has shown is immeasurable.
“At this stage there is a clear argument to be made that Daniel’s death would not have happened had reasonable steps been taken to address Henry’s repeat offending, especially when considered alongside the conditions of his early release license and criminal background.”
A date for the inquiry has yet to be set.
A COPFS spokesperson said: “The Lord Advocate considers that there are issues surrounding the circumstances of the death which merit further examination in the public interest.
“A Fatal Accident Inquiry is a judicial process which seeks to establish the circumstances of a death and identify what lessons, if any, may be learned.
“The Procurator Fiscal is taking forward the necessary work to initiate the inquiry and Mr Greer’s family will continue to be kept informed of significant developments.”
BBC News
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